In most cases the plane, or display, is of finite size, but the movements of the pointer are usually not limited in space. This means that the movements of the user can drive the position of the object beyond the limits of the display. First, we consider the case of a conventional 2D computer mouse that the user moves across the horizontal desk surface to move the cursor on a display or screen. It is known that when the user moves too far in a certain direction, the actual cursor stops and remains at the screen border because the cursor cannot move beyond the limits of the screen. The advantage of this principle is that it is quite easy to use the objects at the edges of the screen, such as the scroll bar or the close button, since they seem to have an infinite width (in the direction beyond the screen). Therefore, the user does not have to perform a precise movement to select these objects.
A problem with the behaviour of the 2D mouse at the screen border is that the cursor starts moving as soon as the user reverses direction. This creates an offset between the position of the cursor and the position of the mouse compared to when the user moved the pointer and the position of the cursor was about to leave the screen. A commonly used correction when using a 2D computer mouse is to have the user lift and displace the mouse to cancel this offset.
The ‘lift and displace’ method does not work for a 3D pointer, which is not supported by e.g. a desk surface and can be freely moved in space. Therefore, other algorithms are preferred for 3D pointers to map the movement of the pointer to the movement of the object on the screen.
As an alternative, the position of the object may be tracked beyond the limits of the screen. This means that the position of the object is calculated as if the screen would be infinite, but the user is not actually able to see the object/cursor. When the calculated position is again within the screen limits, the cursor appears again because it can be shown on the screen. The problem with this solution is that it is more difficult and less user friendly to control e.g. the scroll bar on the side of the screen, or target the buttons on the top right corner, like the close button, because they no longer have an ‘infinite’ size. Moreover, because the user does not have any visual feedback as long as the cursor is outside the screen limits, it is not easy to predict exactly where and when the cursor will re-enter the screen.